The game called the Towers of Hanoi was invented by the French mathematician Edouard Lucas in 1883 and since then it has been both a popular puzzle and a well-known mathematical problem that is an excellent illustration of the general concept of recursion. This puzzle is known by most mathematicians and a very large number of people who like either puzzles or elementary mathematical problems.
The original Towers of Hanoi puzzle is illustrated in FIG. 1. The Towers of Hanoi consists of seven disks 110A-110G of different sizes which during the solution of the puzzle are arranged in three stacks 120, 130, 140. When the game starts, all of the disks 110A-110G are in a single stack 120 arranged by size, so that largest disk 110G is at the bottom of the stack 120. The goal of the puzzle is to move all of the disks 110A-110G to the third stack 140. This must be achieved by observing the following rules:
(1) one move consists of taking the topmost disk from a stack and putting it on another stack--either starting a new stack or placing it on top of other disks on the second stack. PA1 (2) the move described in (1) can be performed only if all of the disks in the second stack are larger than the disk being moved--i.e. a larger disk can never be placed on top of a smaller disk.
The actual realization of the puzzle usually consists of a base 150, three pegs 120, 130, 140, and disks 110A-110G that can be put on the pegs 120, 130, 140. Puzzles constructed this way are available in some toy stores.
Unlike other mechanical puzzles, like Rubik's cube, or Lloyd's 15, this puzzle requires the player to observe some rules, which are not guaranteed by the mechanics of the puzzle. It is possible to cheat or make mistakes and get to the solution in an easier way, without destroying or taking apart the mechanical structure of the puzzle. This is a disadvantage, since some of the potential players, e.g. children do not like to memorize and observe rules. Some of the attraction of mechanical puzzles is the mechanical structure that forces the rules on the player. This is missing in the prior art implementations of this game.